On Global Dimensions of $A_n$-Type Finite Dimensional Algebras
Received:August 23, 2014  Revised:March 04, 2015
Key Words: global dimension   finite dimensional $k$-algebra   quiver   admissible ideal  
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11371307).
Author NameAffiliation
Ruchen HOU School of Mathematics and Information Science, Yantai University, Shandong 264005, P. R. China 
Hits: 2517
Download times: 2025
      A technique is provided to explicitly describe global dimensions of all $A_{n}$-type finite dimensional $k$-algebras for $k$ an algebraic closed field. All possible global dimensions of all $A_n$-type finite dimensional algebras are explicitly presented. In particular, it is pointed out that the maximum is $n-1$, and the minimum is $1$ for $n>1$.
View Full Text  View/Add Comment  Download reader